prob.ipynb

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   "source": [
    "# Classes to represent Probability Space"
   ]
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    "class Event:\n",
    "    def __init__(self, pred, condition=None):\n",
    "        self.pred = pred\n",
    "        self.condition = condition\n",
    "        \n",
    "    def __or__(self, pred):\n",
    "        return Event(self.pred, pred.pred)"
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    "class Probability:\n",
    "    def __init__(self, sample_space):\n",
    "        self.sample_space = sample_space\n",
    "        \n",
    "    def __call__(self, event):\n",
    "        if event.condition:\n",
    "            num = len({x for x in self.sample_space if event.pred(x) and event.condition(x)})\n",
    "            den = len({x for x in self.sample_space if event.condition(x)})\n",
    "            return num / den\n",
    "        else:\n",
    "            num = len({x for x in self.sample_space if event.pred(x)})\n",
    "            den = len(self.sample_space)\n",
    "            return num/den"
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   "source": [
    "# Sample Usecases"
   ]
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   "source": [
    "# dice has 6 outcomes\n",
    "sample_space = {1,2,3,4,5,6}\n",
    "p = Probability(sample_space)"
   ]
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   "source": [
    "# to find the probability of even numbers\n",
    "is_even = Event(lambda x : x%2 == 0)\n",
    "p(is_even)"
   ]
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   "source": [
    "# to find the probability of even numbers given it is > 3\n",
    "greater_3 = Event(lambda x : x>3)\n",
    "p(is_even | greater_3) # 2/3"
   ]
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   "source": [
    "# Questions 1, 2"
   ]
  },
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   "source": [
    "sample_space = {\"GG\",\"GB\",\"BG\",\"BB\"}\n",
    "p = Probability(sample_space1)"
   ]
  },
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   "execution_count": 77,
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   "source": [
    "older_is_boy = Event(lambda x: x[0] == \"B\")\n",
    "at_least_one_boy = Event(lambda x: \"B\" in x)\n",
    "both_boy = Event(lambda x: x.count(\"B\") == 2)"
   ]
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   "execution_count": 78,
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   "source": [
    "p(both_boy | older_is_boy)"
   ]
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   "source": [
    "p(both_boy | at_least_one_boy)"
   ]
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   "source": [
    "# Question 3"
   ]
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   "source": [
    "sample_space = {f\"{c1}{d1}{c2}{d2}\" \n",
    "                for c1 in [\"B\",\"G\"] for d1 in [1,2,3,4,5,6,7]\n",
    "                for c2 in [\"B\",\"G\"] for d2 in [1,2,3,4,5,6,7]}\n",
    "p2 = Probability(sample_space) "
   ]
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   "source": [
    "at_least_one_on_tues = Event(lambda x: \"B2\" in x)"
   ]
  },
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   "execution_count": 82,
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   ],
   "source": [
    "p2(both_boy | at_least_one_on_tues)"
   ]
  }
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